Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 10 to 4 computations (60% saved)

sample457.0ms (53.3%)

Memory

37.5MiB live, 502.3MiB allocated; 78ms collecting garbage

Samples

302.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 146.0ms

ival-hypot: 144.0ms (98.5% of total)

adjust: 2.0ms (1.4% of total)

Bogosity

preprocess59.0ms (6.8%)

Memory

-3.1MiB live, 41.9MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	38	19
2	117	19
3	209	19
4	601	19
5	3247	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.4%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 10 to 8 computations (20% saved)

series3.0ms (0.3%)

Memory

3.1MiB live, 3.0MiB allocated; 0ms collecting garbage

Counts

4 → 5

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 x x)
x

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (+ (* x x) (* x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x) x)
1.0ms	x	@	-inf	((sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x) x)
1.0ms	x	@	0	((sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x) x)

rewrite67.0ms (7.8%)

Memory

-25.1MiB live, 24.5MiB allocated; 55ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	70
0	22	59
0	66	50

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

9 → 44

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 x x)
x
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (+ (* x x) (* x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))

Outputs
(pow.f64 (*.f64 x (+.f64 x x)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (fabs.f64 x))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (neg.f64 x))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) x)
(hypot.f64 (fabs.f64 x) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) (neg.f64 x))
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 (neg.f64 x) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (neg.f64 x) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 x x))) (.f64 x x))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x (+.f64 x x))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 x x) (.f64 x x)))
(/.f64 (+.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (fma.f64 (.f64 x x) (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 x x))
(fma.f64 x x (*.f64 x x))
(-.f64 (.f64 x x) (.f64 (neg.f64 x) x))
(-.f64 (.f64 x x) (neg.f64 (.f64 x x)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
x
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (+ (* x x) (* x x)) (*.f64 x (+.f64 x x)))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

eval4.0ms (0.4%)

Memory: 5.3MiB live, 5.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 202 to 96 computations (52.5% saved)

prune2.0ms (0.2%)

Memory

2.8MiB live, 2.8MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	4	42

Accuracy

100.0%

Counts

42 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	54.4%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	2.2%	#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Compiler

Compiled 25 to 23 computations (8% saved)

series5.0ms (0.6%)

Memory

6.1MiB live, 6.1MiB allocated; 0ms collecting garbage

Counts

11 → 5

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
(+.f64 x x)
(hypot.f64 x x)

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (neg (* (sqrt 2) x)) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx x #s(hole binary64 x))
#s(approx (* x (+ x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((sqrt (+ (* x x) (* x x))) (neg (* (sqrt 2) x)) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (+ (* x x) (* x x))) (sqrt (* x (+ x x))) (* x (+ x x)) (+ x x) (sqrt (+ (* x x) (* x x))))
2.0ms	x	@	inf	((sqrt (+ (* x x) (* x x))) (neg (* (sqrt 2) x)) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (+ (* x x) (* x x))) (sqrt (* x (+ x x))) (* x (+ x x)) (+ x x) (sqrt (+ (* x x) (* x x))))
1.0ms	x	@	0	((sqrt (+ (* x x) (* x x))) (neg (* (sqrt 2) x)) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (+ (* x x) (* x x))) (sqrt (* x (+ x x))) (* x (+ x x)) (+ x x) (sqrt (+ (* x x) (* x x))))

Time

Variable

Point

Expression

2.0ms

-inf

((sqrt (+ (* x x) (* x x))) (neg (* (sqrt 2) x)) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (+ (* x x) (* x x))) (sqrt (* x (+ x x))) (* x (+ x x)) (+ x x) (sqrt (+ (* x x) (* x x))))

2.0ms

inf

((sqrt (+ (* x x) (* x x))) (neg (* (sqrt 2) x)) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (+ (* x x) (* x x))) (sqrt (* x (+ x x))) (* x (+ x x)) (+ x x) (sqrt (+ (* x x) (* x x))))

1.0ms

((sqrt (+ (* x x) (* x x))) (neg (* (sqrt 2) x)) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (+ (* x x) (* x x))) (sqrt (* x (+ x x))) (* x (+ x x)) (+ x x) (sqrt (+ (* x x) (* x x))))

rewrite30.0ms (3.5%)

Memory

-31.4MiB live, 18.3MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	88
0	38	84
0	101	84

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

16 → 81

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
(+.f64 x x)
(hypot.f64 x x)
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (neg (* (sqrt 2) x)) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx x #s(hole binary64 x))
#s(approx (* x (+ x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
(.f64 (.f64 #s(literal -1 binary64) x) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) x)
(.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal -1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(fabs.f64 (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
x
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(fabs.f64 (sqrt.f64 (*.f64 (+.f64 x x) x)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (fabs.f64 x))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (neg.f64 x))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) x)
(hypot.f64 (fabs.f64 x) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) (neg.f64 x))
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 (neg.f64 x) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (neg.f64 x) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 x x))) (.f64 x x))
(*.f64 (+.f64 x x) x)
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x (+.f64 x x))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 x x) (.f64 x x)))
(/.f64 (+.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (fma.f64 (.f64 x x) (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 x x))
(fma.f64 x x (*.f64 x x))
(-.f64 (.f64 x x) (.f64 (neg.f64 x) x))
(-.f64 (.f64 x x) (neg.f64 (.f64 x x)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x x)) x)
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 x x) (.f64 x x)) (-.f64 x x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))))
(-.f64 x (neg.f64 x))
(+.f64 x x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(fabs.f64 (sqrt.f64 (*.f64 (+.f64 x x) x)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (fabs.f64 x))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (neg.f64 x))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) x)
(hypot.f64 (fabs.f64 x) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (fabs.f64 x) (fabs.f64 x))
(hypot.f64 (fabs.f64 x) (neg.f64 x))
(hypot.f64 (fabs.f64 x) x)
(hypot.f64 (neg.f64 x) (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (neg.f64 x) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (neg (* (sqrt 2) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
#s(approx x x)
#s(approx (* x (+ x x)) (*.f64 (+.f64 x x) x))
#s(approx (+ x x) (+.f64 x x))

eval5.0ms (0.6%)

Memory: 7.4MiB live, 7.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 265 to 144 computations (45.7% saved)

prune3.0ms (0.3%)

Memory

4.1MiB live, 4.1MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	56	5	61

Accuracy

100.0%

Counts

61 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	54.4%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.2%	#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Compiler

Compiled 30 to 28 computations (6.7% saved)

series3.0ms (0.4%)

Memory

3.9MiB live, 3.9MiB allocated; 0ms collecting garbage

Counts

5 → 10

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
x
(sqrt.f64 (+.f64 x x))
(+.f64 x x)

Outputs
#s(approx (* (sqrt x) (sqrt (+ x x))) #s(hole binary64 (* (sqrt x) (sqrt (* 2 x)))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ x x)) #s(hole binary64 (sqrt (* 2 x))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (* (sqrt x) (sqrt (+ x x))) #s(hole binary64 (* (pow x 2) (* (sqrt (/ 1 x)) (sqrt (/ 2 x))))))
#s(approx (sqrt x) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 x)))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 x))))))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (+ x x))
1.0ms	x	@	-inf	((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (+ x x))
1.0ms	x	@	inf	((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (+ x x))

rewrite22.0ms (2.6%)

Memory

15.4MiB live, 15.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	121
0	41	114
0	118	114

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

15 → 28

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 x)
x
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
#s(approx (* (sqrt x) (sqrt (+ x x))) #s(hole binary64 (* (sqrt x) (sqrt (* 2 x)))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ x x)) #s(hole binary64 (sqrt (* 2 x))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (* (sqrt x) (sqrt (+ x x))) #s(hole binary64 (* (pow x 2) (* (sqrt (/ 1 x)) (sqrt (/ 2 x))))))
#s(approx (sqrt x) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 x)))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 x))))))

Outputs
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
x
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(pow.f64 (+.f64 x x) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 x x))
(fabs.f64 (sqrt.f64 (+.f64 x x)))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 x x)) x)
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 x x) (.f64 x x)) (-.f64 x x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))))
(-.f64 x (neg.f64 x))
(+.f64 x x)
#s(approx (* (sqrt x) (sqrt (+ x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx x x)
#s(approx (sqrt (+ x x)) (sqrt.f64 (+.f64 x x)))
#s(approx (+ x x) (+.f64 x x))
#s(approx (* (sqrt x) (sqrt (+ x x))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) x))) (*.f64 x x)))
#s(approx (sqrt x) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x))
#s(approx (sqrt (+ x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x))
#s(approx (sqrt x) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)))
#s(approx (sqrt (+ x x)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)))

eval2.0ms (0.2%)

Memory: 2.3MiB live, 2.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 129 to 86 computations (33.3% saved)

prune2.0ms (0.2%)

Memory

2.5MiB live, 2.5MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	21	6	27

Accuracy

100.0%

Counts

27 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	99.3%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)))
✓	54.4%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.2%	#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Compiler

Compiled 40 to 38 computations (5% saved)

series6.0ms (0.7%)

Memory

-31.6MiB live, 10.4MiB allocated; 4ms collecting garbage

Counts

8 → 12

Calls

Call 1

Inputs
(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)))
(sqrt.f64 x)
x
#s(approx (sqrt (+ x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)
(sqrt.f64 (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)

Outputs
#s(approx (* (sqrt x) (sqrt (+ x x))) #s(hole binary64 (* (sqrt x) (sqrt (* 2 x)))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ x x)) #s(hole binary64 (sqrt (* 2 x))))
#s(approx (sqrt (/ 2 x)) #s(hole binary64 (/ (sqrt (* 2 x)) x)))
#s(approx (/ 2 x) #s(hole binary64 (/ 2 x)))
#s(approx (* (sqrt x) (sqrt (+ x x))) #s(hole binary64 (* (pow x 2) (* (sqrt (/ 1 x)) (sqrt (/ 2 x))))))
#s(approx (sqrt x) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 x)))))
#s(approx (sqrt (/ 2 x)) #s(hole binary64 (sqrt (/ 2 x))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 x))))))

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (* (sqrt (/ 2 x)) x) (sqrt (/ 2 x)) (/ 2 x) 2)
1.0ms	x	@	inf	((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (* (sqrt (/ 2 x)) x) (sqrt (/ 2 x)) (/ 2 x) 2)
1.0ms	x	@	0	((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (* (sqrt (/ 2 x)) x) (sqrt (/ 2 x)) (/ 2 x) 2)

Time

Variable

Point

Expression

4.0ms

-inf

((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (* (sqrt (/ 2 x)) x) (sqrt (/ 2 x)) (/ 2 x) 2)

1.0ms

inf

((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (* (sqrt (/ 2 x)) x) (sqrt (/ 2 x)) (/ 2 x) 2)

1.0ms

((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (* (sqrt (/ 2 x)) x) (sqrt (/ 2 x)) (/ 2 x) 2)

rewrite25.0ms (3%)

Memory

32.3MiB live, 32.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	166
0	48	160
0	131	160

Stop Event

1×	iter-limit
1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

20 → 30

Calls

Call 1

Inputs
(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)))
(sqrt.f64 x)
x
#s(approx (sqrt (+ x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)
(sqrt.f64 (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
#s(approx (* (sqrt x) (sqrt (+ x x))) #s(hole binary64 (* (sqrt x) (sqrt (* 2 x)))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ x x)) #s(hole binary64 (sqrt (* 2 x))))
#s(approx (sqrt (/ 2 x)) #s(hole binary64 (/ (sqrt (* 2 x)) x)))
#s(approx (/ 2 x) #s(hole binary64 (/ 2 x)))
#s(approx (* (sqrt x) (sqrt (+ x x))) #s(hole binary64 (* (pow x 2) (* (sqrt (/ 1 x)) (sqrt (/ 2 x))))))
#s(approx (sqrt x) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 x)))))
#s(approx (sqrt (/ 2 x)) #s(hole binary64 (sqrt (/ 2 x))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 x))))))

Outputs
(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)))
(.f64 #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)) (sqrt.f64 x))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
x
#s(approx (sqrt (+ x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)
(*.f64 x (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(sqrt.f64 (/.f64 #s(literal 2 binary64) x))
(fabs.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -2 binary64) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 x #s(literal 2 binary64)))
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
#s(approx (* (sqrt x) (sqrt (+ x x))) (sqrt.f64 (*.f64 x (+.f64 x x))))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx x x)
#s(approx (sqrt (+ x x)) (sqrt.f64 (+.f64 x x)))
#s(approx (sqrt (/ 2 x)) (/.f64 (sqrt.f64 (+.f64 x x)) x))
#s(approx (/ 2 x) (/.f64 #s(literal 2 binary64) x))
#s(approx (* (sqrt x) (sqrt (+ x x))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) x))) (*.f64 x x)))
#s(approx (sqrt x) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x))
#s(approx (sqrt (+ x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x))
#s(approx (sqrt (/ 2 x)) (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))
#s(approx (sqrt x) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)))
#s(approx (sqrt (+ x x)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)))

eval2.0ms (0.2%)

Memory: 2.8MiB live, 2.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 149 to 101 computations (32.2% saved)

prune3.0ms (0.3%)

Memory

6.7MiB live, 6.7MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	21	6	27

Accuracy

100.0%

Counts

27 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)))
✓	54.4%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.2%	#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Compiler

Compiled 77 to 65 computations (15.6% saved)

regimes19.0ms (2.2%)

Memory

-21.1MiB live, 20.7MiB allocated; 10ms collecting garbage

Counts

7 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)))
(hypot.f64 x x)

Outputs
(hypot.f64 x x)

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	x
2.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 x x)`
100.0%	1	`(+.f64 (.f64 x x) (.f64 x x))`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
100.0%	1	`x`

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes8.0ms (1%)

Memory

16.7MiB live, 16.7MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)))

Outputs
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

Calls

4 calls:

2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.4%	1	`(*.f64 x x)`
99.4%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.4%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.4%	1	`x`

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes6.0ms (0.7%)

Memory

12.6MiB live, 12.6MiB allocated; 0ms collecting garbage

Accuracy

Total -62.2b remaining (-14873.4%)

Threshold costs -62.2b (-14873.4%)

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

(sqrt.f64 (*.f64 x (+.f64 x x)))

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Calls

4 calls:

1.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
1.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
99.3%	1	`(*.f64 x x)`
99.3%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.3%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.3%	1	`x`

Compiler

Compiled 12 to 10 computations (16.7% saved)

derivations4.0ms (0.4%)

Memory

5.0MiB live, 5.0MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 14 to 13 computations (7.1% saved)

preprocess122.0ms (14.2%)

Memory: -46.4MiB live, 53.1MiB allocated; 42ms collecting garbage
Compiler: Compiled 51 to 47 computations (7.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample457.0ms (53.3%)

preprocess59.0ms (6.8%)

series3.0ms (0.3%)

rewrite67.0ms (7.8%)

eval4.0ms (0.4%)

prune2.0ms (0.2%)

series5.0ms (0.6%)

rewrite30.0ms (3.5%)

eval5.0ms (0.6%)

prune3.0ms (0.3%)

series3.0ms (0.4%)

rewrite22.0ms (2.6%)

eval2.0ms (0.2%)

prune2.0ms (0.2%)

series6.0ms (0.7%)

rewrite25.0ms (3%)

eval2.0ms (0.2%)

prune3.0ms (0.3%)

regimes19.0ms (2.2%)

regimes8.0ms (1%)

regimes6.0ms (0.7%)

derivations4.0ms (0.4%)

preprocess122.0ms (14.2%)

end0.0ms (0%)

Profiling